Friends (1994)

Answer: They had already dated and broken up. When they began their online relationship, they were unaware who the other person was.

raywest ★

Answer: Joey has just made an incredibly stupid remark (how would she know how long she's going to live?), so he wonders how Joey is even smart enough to walk. It's just a joke.

Shay

Answer: I agree with the other answers. Another possibility is, Rachel was close friends with both Monica and Mindy in high school. Mindy was likely friends with Monica, and therefore invited her to the wedding along with Rachel, knowing they were roommates. Richard has known the Geller and Green families for years and may also know Mindy's parents and was invited separately. He could be Monica's +1, or she his, but even if both were invited separately, they are still attending as a couple. Monica wasn't invited to Rachel and Barry's wedding because the girls had lost touch after high school and Monica moved to NYC.

raywest ★

Answer: Excellent question, and it's never occurred to me. My best guess would be that Barry/Mindy are aware they're asking a big favour of Rachel and realise it would be an awkward situation for her, so let her invite a friend (Monica) for moral support so there'd be a friendly face there for her.

Jon Sandys ★

Answer: It's never explained, and the writers probably didn't gave it serious thought, just using their presence at the wedding as a plot device. But since, as you say, Monica was not invited to Rachel's wedding, the most logical explanation is that Richard is the invitee, and Monica is his +1. Richard and Barry are both doctors and so could know one another, or perhaps Richard is friends with Barry's, or Mindy's, parents. If the latter, this would not be unbelievable, as Mindy's parents would likely be in the same circle as the Gellers, with whom Richard is close.